It is a freezing late-August afternoon in a not particularly Mozartian part of Vienna. Natascha Kampusch stands before me in her agent's office, shaking my hand. To her left is her agent, Wolfgang Brunner, to her right her translator, Jill Kreuer. Her mouth is very firmly shut, her lips squeezed hard together. I notice a small, discoloured patch of skin on her hand, a wound from a beating that will never completely heal.

"Thank you for meeting me," I say.

She nods, still keeping her mouth tightly closed.

Twelve years ago, when Natascha was 10, she was walking to school (it was the very first occasion her mother had allowed her to walk alone) when she noticed a man standing by a delivery van. He looked neat, conservative. As she passed, he grabbed her and threw her in.

Eight years later, in August 2006, Natascha miraculously reappeared, running terrified through the Vienna suburbs, pale and gaunt, like a beautiful child from a Brothers' Grimm fairytale, having escaped the clutches of the monster. An astonished, infatuated public awaited her first words. They turned out to be complicated and unsettling and not fairytale-like at all.

The admiration turned to disgust and confusion and she began getting hate mail.

And so she has now written a memoir, 3,096 Days, explaining everything. It is a brilliantly insightful dissection of her years in captivity. She's agreed to talk to me about it. But, unnervingly, her mouth is still tightly closed. I glance anxiously at it. Have I flown to Vienna to meet a woman who is psychologically incapable of speaking? And then, to my relief, she says, "Hello."

"Do you find this hard?" I ask her.

"It's difficult," she says.

"Then why do you do it?"

"I want to reclaim the interpretation of my own story," she says.

Natascha Kampusch was born in a council estate on the edge of Vienna. "I was used to dealing with disturbed people," she says. "There were people in the neighbourhood who were alcoholics, some were mentally disturbed. They liked to talk about conspiracy theories. They had failed at life."

Her divorced parents would slap and insult her. By the age of 10 she was a compulsive eater, depressed and lonely. In fact, her last moments of freedom were spent fantasising about suicide. She would throw herself in front of a car and then her mother would be sorry. That was what she was daydreaming about as she walked in the direction of the man standing by the delivery van.

"How do your parents feel about the memoir?" I ask her. "You're quite honest about their cruelty."

There's a small pause. "They haven't read it yet," she says. Still, she adds, she hopes 3,096 Days will dispel the impression people have "that my mother was a very brutal person and that I had a better time of it in the dungeon." However hard her mother was, she was nothing like Priklopil.

Her first words to her kidnapper as she lay in the van: "What size shoes do you wear?"

"What was his shoe size?" she says. "How old was he? Was he married with children? Why didn't he have children? I fired these questions at him."

"Why?" I ask.

"I knew from watching Aktenzeichen XY… ungelöst [Austria's version of Crimewatch] that you must get as much information about a criminal as possible." She smiles, remembering her naivety with fondness.

He drove her to his home in a prosperous suburb called Strasshof and carried her into a tiny cellar room he'd evidently spent a long time preparing. It was beneath a trapdoor in the garage, down some stairs, through a hollowed-out concrete wall hidden on the other side of a small metal hatch concealed behind a cupboard. It was so clandestine and fortified, it took an hour to get inside. It was five by five metres, bare, soundproofed, windowless and filled with the constant irritating rattle of a plastic ventilator fan.

He made to take away her schoolbag. When she asked if she could hold onto it, Priklopil's response was startling. "You could have hidden a transmitter," he said, "and you could use it to call for help."

It was a strange and paranoid statement – 10-year-olds tend not to hide transmitters in their schoolbags. But still, she says, "I was used to grown-ups doing and saying strange things I didn't understand."

She asked him to tuck her in, read her a story and give her a goodnight kiss. All of which he cheerfully did.

In the beginning, their relationship was relatively uncomplicated. Or as uncomplicated as things can be when one half of the duo is locked in a dungeon and the other has to keep the whole convoluted setup a secret from the outside world, including his mother and his best friend, Ernst Holzapfel, both of whom regularly visited the house. He brought her fancy croissants and expensive toys, like train sets. As a coping mechanism, she says, she regressed psychologically to the age of a dependent toddler.

But then things started to get odder. His gifts to her became less thoughtful. "He began giving me presents like mouthwash and scotch tape," she says. "Still, I was very happy to get those presents. I was happy to get any present, even if it was orange juice."

He told her he was an Egyptian god and she decided that the easiest thing to do would be to go along with it.

"In situations when I was being bathed," she says, "I pictured myself being at a spa. When he gave me something to eat, I imagined him as a gentleman, that he was doing all this for me to be gentlemanly. Serving me." She pauses. "I thought it was very humiliating to be in that situation."

By her early-teenage years, she found being a compliant character in his psychotic delusions more difficult, so began fighting back with small acts of rebellion. She adamantly refused, for instance, to call him "Maestro". It was a weirdness too far.

"I thought it was ridiculous and silly," she says. "But I recognised similar behaviour from preschool. One child would say, 'I'm the ruler. I'm the king.' Or, 'I'm a princess. You have to listen to me, you have to do as I say.' This was a similar kind of megalomania."

And so now it was Priklopil's turn to adapt to a new situation. His captive was no longer a docile plaything. Unfortunately, he decided the solution was to break her completely and then remould her.

"He wanted to show more and more that he was stronger than I was, that I was someone who had to obey without question."

He began persistently and violently beating her up, denying her food, keeping her in darkness for long stretches, and on and on. He constructed an intercom so he could lie awake all night yelling insults at her from his bedroom upstairs. He had trained as an engineer at Siemens, hence his technical abilities.

"When we ate together, he always allowed himself a much bigger portion," she says. "I saw that I had no rights. Also, he began to see me as a person who could do a lot of hard manual labour."

He started bringing her upstairs to clean his house. She had to do this half naked, her gaze lowered. She was only allowed to speak when spoken to, or he'd beat her up. She writes in 3,096 Days that the one thing she won't discuss is the sexual abuse, but that it was minor, and even when he began manacling her to his bed all he wanted to do was cuddle.

She puts her survival down to a moment that occurred when she was 12. There being no sane, solid adults in her life, she decided to become her own adult. Her 18-year-old self appeared to her in a vivid vision. She told her, "I will get you out of here, I promise you. Right now you are too small. But when you turn 18 I will overpower the kidnapper and free you from your prison."

The beatings continued over the next six years. Sometimes the only way to avert them was to repeatedly, almost mockingly, punch herself in the face, until he begged her to stop. There were suicide attempts, too. She tried to slit her wrists with a knitting needle when she was 14. But there were also moments of warmth. Sometimes he would apologise to her, buy her gifts, tell her his dreams of their life together.

"I think he really trusted me," she says. "He was able to communicate with me, to act out his illness. I think he wanted to create his own little perfect world with a person who could be there just for him."

His vision was for her to be a kind of beautiful Aryan servant and adoring companion. He told her the Jews were responsible for 9/11, he dyed her hair blonde and – after convincing her that any escape attempt would mean death for her and him and scores of bystanders – he took her skiing. The Aryan girl skiing down a hill at his side, "like Leni Riefenstahl had been the director of the film", she laughs.

In fact, he took her on 13 day trips in all, to a chemist, a hardware store, but mostly to empty rental flats he was renovating for his friend, Ernst Holzapfel. He made her do the manual work. She was too scared to run away, to say anything to the various strangers she encountered – the chemist, the policeman who stopped the car at a roadblock.

Then she turned 18. And when she did she looked at him and said, "You have brought a situation upon us in which only one of us can make it through alive. I really am grateful to you for not killing me and for taking such good care of me. That is very nice of you. But you can't force me to stay with you. I am my own person with my own needs. This situation must come to an end."

She closed her eyes expecting a beating, but it didn't come. Instead, she opened them to see him looking sad, defeated.

"I think he understood that I was at the end of my strength," she says. "He had brought me to the brink, I had no energy left, but in a way that empowered me. He had nothing to counter it with."

And then, a few weeks later, he left her alone in the garden for a moment while he took a telephone call, and she just walked out of the gate.

Then she started running, frantically. She pleaded with passers-by to help her, but they ignored her. Finally she found someone who was willing to call the police.

"Do you think he'd resigned himself to you escaping?" I ask.

"It's possible he saw it coming," she says. "It's possible he wished it would happen."

Of course it must have all become a terrible burden for him: the stress of keeping a secret slave. He went to his friend Ernst Holzapfel. They drove around Vienna for three hours and he confessed everything. "I am a kidnapper and a rapist," he told him.

And then Holzapfel let him out of the car and Priklopil lay down on some railway tracks, until a train ran over his head.

At first Natascha was inundated with offers of help, albeit sometimes odd ones: "You could live with me and help with the housework. I'm offering board, wages and lodging. Although I'm married, I'm sure we'll find an arrangement," wrote one.

But the offers stopped, she says, when she refused to play the role of a victim – a weak girl in need of help – and instead tried to explain to interviewers the nuances of their relationship. That wasn't the story people wanted to hear, so they dismissed her as suffering from Stockholm Syndrome – a label intended, she says, to deny her the ability to judge her own experiences.

"I find it very natural that you would adapt yourself to identify with your kidnapper," she says. "Especially if you spend a great deal of time with that person. It's about empathy, communication. Looking for normality within the framework of a crime is not a syndrome. It is a survival strategy." She pauses. "But people get annoyed when I say this. Some say I should be locked up again, that it isn't really special to have been locked up like that, that I liked it, that it was good for me."

Natascha has bought the Strasshof house to prevent it from becoming a shrine for crazy fans. She says she finds her sort of fame "bothersome and disturbing. I knew, when I was in the dungeon, that the story would make me famous, but I thought it would be a more positive experience, like winning the Olympics. You're in the media once, people admire you, and then it's over and done with. I never thought I'd meet so many unpleasantly curious people who refuse to keep their distance from me, who are uneducated. I have many personal complexes as well, so being such a well-recognised figure just adds to that."

"What kind of complexes?" I ask.

"Insecurities. Why are people staring at me so strangely and treating me so weirdly? And then I remember, oh yeah. People recognise me."

For a while she, unexpectedly, became a TV chatshow host. "I always wanted to interview people," she says. "When I was imprisoned, I listened to the radio and I admired the interviewers." She pauses and smiles. "And I have certainly learned how to engage with people one on one. I was forced to listen to him, which I think was very positive, because a lot of people my age are not good at listening."

"It must have been a good lesson in human nature," I say. "So are you going to be a journalist?"

"A psychologist," she replies. "Although before I do that I would like to learn two trades: goldsmith and shoemaker."

"Everything a girl wants," says her agent from across the table.

I ask if she gets flashbacks. She shrugs. "I don't forget it, but right now it's not important. I want to live in the now. But sometimes, yes, I have flashbacks."

"What brings them on?"

"When I've been troubled by a situation where somebody acts in a similar way. Like in my private life. I see men put women down and act possessively towards them. I get flashbacks when people try to make me eat something when I'm not hungry. In the dungeon, food was withheld from me, but when they do the opposite it robs me of my dignity."

Does she tell them, "You're acting like the kidnapper"?

"Sometimes," she says.

Does that make them back away?

"Yes," she smiles.

And now there's the memoir. Did trying to get inside his head help her psychologically?

"I like to do it very much," she replies. "In fact, I probably like to do it too much, which is why I've gone back to a therapist. I like to put myself in people's shoes and try to feel what they feel. For instance, if I'm in love with someone, I constantly think, 'Why did he say it that way? Did he mean it that way? What happened in his childhood? Why is he acting that way?'"

"But, of course, in your kidnapper's case, you're trying to get inside a head that's completely jumbled and disordered," I say.

"But he trusted me. He was able to open himself up to me and show me his ideas and visions, even though they were sick visions and ideas."

She pauses. "I don't want to engage in talk-show psychology, but I think it all happened because he was too conservative on the outside, too well-adjusted and conformist, and I think that's why he committed the crime. He had this border between what was permitted by society and what his personal desires were, and he was unable to reconcile the two."

And then – tired of talking about it all – she plays everyone in the room a song on her iPhone and sprays some of her new perfume in the air.

• 3,096 Days, by Natascha Kampusch, is published by Penguin at £7.99. To order a copy, visit the Guardian Bookshop.